Two-scale Neural Networks for Partial Differential Equations with Small Parameters
This addresses computational challenges in PDE solving for scientific computing, but it is incremental as it builds on existing physics-informed neural networks.
The authors tackled solving partial differential equations with small parameters by proposing a two-scale neural network method that incorporates these parameters directly into the architecture, achieving reasonable accuracy in capturing large derivative features in numerical examples.
We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of neural networks. The proposed method enables solving PDEs with small parameters in a simple fashion, without adding Fourier features or other computationally taxing searches of truncation parameters. Various numerical examples demonstrate reasonable accuracy in capturing features of large derivatives in the solutions caused by small parameters.